In just 12 minutes the paraxial ray trace equations are cast into 2x2 reflection, refraction, and transfer matrices and written into a MATLAB function. This method is described in most optics textbooks, for example Hecht Chapter 6 and Pedrotti Chapter 18. As a simple example, the ray trace matrices are applied to a thick lens in order to determine its effective focal length, its back focal length, and its principal plane location. The slider and the play-pause button were meant for videos like this.
Introduction to the paraxial ray trace equations https://youtu.be/g-mPisltcRQ
Optical Design Playlist: https://www.youtube.com/playlist?list=PLmfHzApbF5dbx_S_h9A13uLm4LVK0f6XK
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